Optical security system using fourier plane encoding

1. A method of verifying the authenticity of an object, the method comprising: encoding a primary image; convolving the encoded primary image with a random code, generating thereby a first reference image; transforming the first reference image; and correlating the first reference image with a second reference image; wherein convolving the encoded primary image with a random code comprises convolving the encoded primary image with a random code that is the Fourier transform of a phase-only uniform random distribution.

2. The method as set forth in claim 1 wherein encoding the primary image comprises phase encoding the primary image.

4. The method as set forth in claim 1 wherein convolving the encoded primary image with a random code comprises convolving the encoded primary image with a filter that is matched to the random code.

5. The method as set forth in claim 1 wherein transforming the first reference image comprises Fourier transforming the first reference image.

7. The method as set forth in claim 6 wherein generating a phase-only reference image includes binarizing the phase-only reference image according to the equation r B _ ⁡ ( x , y ) = r ⁡ ( x , y )  r ⁡ ( x , y )  where r B _ ⁡ ( x , y ) = { - 1 ⁢ ⁢ if ⁢ ⁢ Re ⁡ [ r ⁡ ( x , y ) ] < 0 1 ⁢ ⁢ if ⁢ ⁢ Re ⁡ [ r ⁡ ( x , y ) ] ≥ 0 , wherein r B (x,y) is the binarized phase-only reference image and wherein Re[r(x,y)] denotes the real part of r(x,y).

8. The method as set forth in claim 1 wherein correlating the first transformed reference image with a second reference image comprises transforming the second reference image.

9. The method as set forth in claim 8 wherein correlating the first transformed reference image with a second reference image comprises generating a joint power spectrum of the first transformed reference image and the second transformed reference image.

10. The method as set forth in claim 9 further comprising: applying a threshold function equal to the sum of the self product terms of the joint power spectrum to joint power spectrum, generating thereby a modified joint power spectrum; applying a k-th power law nonlinear transformation to the modified joint power spectrum; and analyzing the peaks of the correlation of the modified joint power spectrum of the first reference image and the second reference image; wherein the presence of a single peak indicates the authenticity of the object and the presence of no peaks indicates the lack of authenticity of the object.

11. The method as set forth in claim 10 wherein performing the correlation of the modified joint power spectrum comprises: inverse Fourier transforming the modified joint power spectrum; and squaring the modulus of the inverse Fourier transform of the modified joint power spectrum.

12. The method as set forth in claim 10 wherein k lies within the interval between zero and one inclusive.

13. The method as set forth in claim 1 further comprising affixing the second reference image to an object, the authenticity of which is to be verified.

14. A method of generating a reference image for verifying the authenticity of an image, the method comprising: encoding a primary image; convolving the encoded primary image with a random code, generating thereby a reference image; transforming the reference image; wherein convolving the encoded primary image with a random code comprises convolving the encoded primary image with a random code that is the Fourier transform of a phase-only uniform random distribution.

15. The method as set forth in claim 14 wherein encoding the primary image comprises phase encoding the primary image.

17. The method as set forth in claim 14 wherein convolving the encoded primary image with a random code comprises convolving the encoded primary image with a filter that is matched to the random code.

18. The method as set forth in claim 14 wherein transforming the reference image comprises Fourier transforming the reference image.

19. A method of verifying the authenticity of an object, the method comprising: encoding a primary image; convolving the encoded primary image with a random code, generating thereby a first reference image; transforming the first reference image; and correlating the first reference image with a second reference image; wherein convolving the encoded primary image with a random code comprises convolving the encoded primary image with a filter that is matched to the random code.

21. A method of verifying the authenticity of an object, the method comprising: encoding a primary image; convolving the encoded primary image with a random code, generating thereby a first reference image; transforming the first reference image; and correlating the first reference image with a second reference image, wherein correlating the first transformed reference image with a second reference image comprises: transforming the second reference image; and generating a joint power spectrum of the first transformed reference image and the second transformed reference image; applying a threshold function equal to the sum of the self product terms of the joint power spectrum to joint power spectrum, generating thereby a modified joint power spectrum; applying a k-th power law nonlinear transformation to the modified joint power spectrum; and analyzing the peaks of the correlation of the modified joint power spectrum of the first reference image and the second reference image; wherein the presence of a single peak indicates the authenticity of the object and the presence of no peaks indicates the lack of authenticity of the object; and performing the correlation of the modified joint power spectrum comprises: inverse Fourier transforming the modified joint power spectrum; and squaring the modulus of the inverse Fourier transform of the modified joint power spectrum.